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Entropic properties of D-dimensional Rydberg systems

Author

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  • Toranzo, I.V.
  • Puertas-Centeno, D.
  • Dehesa, J.S.

Abstract

The fundamental information-theoretic measures (the Rényi Rp[ρ] and Tsallis Tp[ρ] entropies, p>0) of the highly-excited (Rydberg) quantum states of the D-dimensional (D>1) hydrogenic systems, which include the Shannon entropy (p→1) and the disequilibrium (p=2), are analytically determined by use of the strong asymptotics of the Laguerre orthogonal polynomials which control the wavefunctions of these states. We first realize that these quantities are derived from the entropic moments of the quantum-mechanical probability ρ(r→) densities associated to the Rydberg hydrogenic wavefunctions Ψn,l,{μ}(r→), which are closely connected to the Lp-norms of the associated Laguerre polynomials. Then, we determine the (n→∞)-asymptotics of these norms in terms of the basic parameters of our system (the dimensionality D, the nuclear charge and the hyperquantum numbers (n,l,{μ}) of the state) by use of recent techniques of approximation theory. Finally, these three entropic quantities are analytically and numerically discussed in terms of the basic parameters of the system for various particular states.

Suggested Citation

  • Toranzo, I.V. & Puertas-Centeno, D. & Dehesa, J.S., 2016. "Entropic properties of D-dimensional Rydberg systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1197-1206.
    • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:1197-1206
    DOI: 10.1016/j.physa.2016.06.144
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    References listed on IDEAS

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    1. López-Rosa, S. & Manzano, D. & Dehesa, J.S., 2009. "Complexity of D-dimensional hydrogenic systems in position and momentum spaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3273-3281.
    2. Alexander Ivanovich Aptekarev & Dmitry Nikolaevich Tulyakov & Irene Valero Toranzo & Jesús Sanchez Dehesa, 2016. "Rényi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(3), pages 1-12, March.
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